The present invention concerns in general terms the transformation of digital signals, and concerns more particularly symmetrical biorthogonal filters with a compact support and satisfying the requirements for perfect reconstruction.
Such filters are already known. The invention aims to provide novel filters whose coding efficiency, or performance, that is to say the output/distortion ratio, is greater than that of known filters.
To this end, the invention proposes a digital filter, and a corresponding filtering method, adapted to transform an input digital signal into two output digital signals,
the input digital signal including input samples,
the first output digital signal including output samples of odd ranking, each output sample of odd ranking being equal to the input sample of the same ranking decreased by the approximate value of a sum of input samples of even ranking respectively multiplied by first filtering coefficients,
the second output digital signal including output samples of even ranking, each output sample of even ranking being equal to the input sample of the same ranking decreased by the approximate value of a sum of output samples of odd ranking respectively multiplied by second filtering coefficients,
in which
the second filtering coefficients are chosen from all the following sets of coefficients: (5/16, 5/16), (xe2x88x921/16, 5/16, 5/16, xe2x88x921/16) and (1/256, xe2x88x9215/256, 78/256, 78/256, xe2x88x9215/256, 1/256).
These filtering coefficients make it possible to construct a family of analysis filters whose performance is better than that of known filters.
According to a preferred characteristic, the first filtering coefficients are chosen from all the following sets of coefficients: (xc2xd, xc2xd), (xe2x88x921/16, 9/16, 9/16 xe2x88x921/16), (3/256, xe2x88x9225/256, 150/256, 150/256, xe2x88x9225/256, 3/256), (xe2x88x925/2048, 49/2048, xe2x88x92245/2048, 1225/2048, 1225/2048, xe2x88x92245/2048, 49/2048, xe2x88x925/2048).
The filters thus constructed are analysis filters of odd length.
The invention also proposes a filter, and a corresponding filtering method, adapted to transform two input digital signals into one output digital signal,
a first input signal including input samples of odd ranking and a second input signal including input signals of even ranking,
the output digital signal including output samples of even ranking and odd ranking,
each output sample of even ranking being equal to the input sample of the same ranking decreased by the approximate value of a sum of input samples of odd ranking respectively multiplied by third filtering coefficients,
each output sample of odd ranking being equal to the input sample of the same ranking increased by the approximate value of a sum of output samples of even ranking respectively multiplied by fourth filtering coefficients,
in which
the third filtering coefficients are chosen from all the following sets of coefficients: (5/16, 5/16), (xe2x88x921/16, 5/16, 5/16, xe2x88x921/16) and (1/256, xe2x88x9215/256, 78/256, 78/256, xe2x88x9215/256, 1/256).
These filtering coefficients make it possible to construct a family of synthesis filters, corresponding to the above analysis filters, and whose performance is better than that of known synthesis filters.
According to a preferred characteristic, the fourth filtering coefficients are chosen from all the following sets of coefficients: (xc2xd, xc2xd), (xe2x88x921/16, 9/16, 9/16 xe2x88x921/16), (3/256, xe2x88x9225/256, 150/256, 150/256, xe2x88x9225/256, 3/256), and xe2x88x925/2048, 49/2048, xe2x88x92245/2048, 1225/2048, 1225/2048, xe2x88x92245/2048, 49/2048, xe2x88x925/2048).
The filters thus constructed are synthesis filters of odd length.
The invention also proposes a digital filter, and a corresponding filtering method, adapted to transform an input digital signal into two output digital signals,
the input digital signal including input samples,
an intermediate digital signal including intermediate samples of odd ranking, each intermediate sample of odd ranking being equal to the input sample of the same ranking decreased by the approximate value of a sum of input samples of even ranking respectively multiplied by fifth filtering coefficients,
the first output digital signal including output samples of even ranking, each output sample of even ranking being equal to the input sample of the same ranking increased by the approximate value of a sum of intermediate samples of odd ranking respectively multiplied by sixth filtering coefficients,
the second output digital signal including output samples of odd ranking, each output sample of odd ranking being equal to the intermediate sample of the same ranking decreased by the approximate value of a sum of intermediate samples of even ranking respectively multiplied by seventh filtering coefficients,
in which
the seventh filtering coefficients are chosen from all the following sets of coefficients: (5/16, 0, xe2x88x925/16), (xe2x88x921/16, 6/16, 0, xe2x88x926/16, 1/16), and (1/256, xe2x88x9216/256, 93/256, 0, xe2x88x9293/256, 16/256, xe2x88x921/256).
These filtering coefficients make it possible to construct a family of analysis filters whose performance is better than that of known filters.
According to a preferred characteristic, the sixth filtering coefficients are chosen from all the following sets of coefficients: (1/16, xc2xd, xe2x88x921/16), (xe2x88x923/256, 22/256, xc2xd, xe2x88x9222/256, 3/256), and (5/2048, xe2x88x9244/2048, 201/2048, xc2xd, xe2x88x92201/2048, 44/2048, xe2x88x925/2048).
The filters thus constructed are analysis filters of even length.
According to another preferred characteristic, there is a single fifth filtering coefficient and it is equal to one. Implementation is thus simplified.
The invention also concerns a filter, and a corresponding filtering method, adapted to transform two input digital signals into one output digital signal,
a first input signal including input samples of odd ranking and a second input signal including input signals of even ranking,
the output digital signal including output samples of even ranking and odd ranking,
an intermediate digital signal including intermediate samples of odd ranking, each intermediate sample of odd ranking being equal to the input sample of the same ranking decreased by the approximate value of a sum of input samples of even ranking respectively multiplied by eighth filtering coefficients,
each output sample of even ranking being equal to the input sample of the same ranking decreased by the approximate value of a sum of intermediate samples of odd ranking respectively multiplied by ninth filtering coefficients,
each output sample of odd ranking being equal to the input sample of the same ranking increased by the approximate value of a sum of output samples of even ranking respectively multiplied by tenth filtering coefficients,
the eighth filtering coefficients are chosen from all the following sets of coefficients: (5/16, 0, xe2x88x925/16), (xe2x88x921/16, 6/16, 0, xe2x88x926/16, 1/16), and (1/256, xe2x88x9216/256, 93/256, 0, xe2x88x9293/256, 16/256, xe2x88x921/256).
These filtering coefficients make it possible to construct a family of synthesis filters, corresponding to the above analysis filters, and whose performance is better than that of known filters.
According to a preferred characteristic, the ninth filtering coefficients are chosen from all the following sets of coefficients: (1/16, xc2xd, xe2x88x921/16), (xe2x88x923/256, 22/256, xc2xd, xe2x88x9222/256, 3/256), and (5/2048, xe2x88x9244/2048, 201/2048, xc2xd, xe2x88x92201/2048, 44/2048, xe2x88x925/2048).
The filters thus constructed are synthesis filters of even length.
According to another preferred characteristic there is a single tenth filtering coefficient and it is equal to one. Implementation is thus simplified.
According to preferred and alternative characteristics, the approximate value is the identity function, or the approximate value is a function of a real variable which supplies the integer which is closest to the variable, or the approximate value is a function of a real variable which supplies the integer below the variable, or the approximate value is a function of a real variable which supplies the integer higher than the variable, or again the approximate value is a function of a real variable broken down into sub-variables, the sum of which is equal to the variable, which supplies a sum of approximate values of the sub-variables, each of the approximate values of the sub-variables being as previously defined.
The invention also concerns a signal processing device including the filter as previously defined, or the means of implementing the corresponding method.
The invention also concerns a signal processing device having at least two filters as previously defined, the output signal of one of the filters being the input signal of the other filter.
The invention also concerns a digital apparatus including the signal processing device.
The advantages of the signal processing device and of the digital apparatus are identical to those disclosed previously.
An information storage means which can be read by a computer or microprocessor, whether or not integrated into the device, possibly removable, stores a program implementing the filtering method.